The homogenised model is significantly more complex than the DFN model because of the greater number of spatial dimensions and the more complicated geometry. In light of the geometrical complexity of the problem, especially at the particle level, it is usually discretised using the Finite Element Method (FEM) which can readily be adapted to such geometries [1]}. In addition, certain limitations that could have been a cause for concern in the DFN model are critical here. The first issue is that of computing effective transport properties. In the DFN model the microstructure is assumed to consist of spherical particles, and therefore effective transport properties can be calculated, or estimated, from pre-existing results based on spherical packings (e.g. Bruggeman correlation [2]}, [3]} or Rayleigh method [4]}, [5]}), but for the homogenised model these properties must be computed from imaging data or from idealised (albeit perhaps non-spherical) geometries. This leads us to the next issue which is: how strong is the separation of scales in a typical porous electrode geometry? Some methods to compute effective transport parameters are based on the assumption that there is a clear separation between the cell and particle length scales [6]}, [7]}. However, for real batteries this separation of scales is not so clear (e.g. particle radius \(\sim 5\)  \(\mu \) m and electrode thickness \(\sim 80\)  \(\mu \) m, see [8]}) and, therefore, the estimated parameters might be questionable. Finally, another limitation of the homogenised model is that some of the new states introduced (such as the lithium distribution within particles, which now is non-symmetric) cannot be observed and therefore many of the outputs of the model cannot be validated.
